Constrained optimization for well placement planning

ABSTRACT

A method, apparatus and program product utilize a constrained optimization framework to generate a well placement plan based on a reservoir model. Candidate well placement plans are generated from control vectors proposed by an optimization engine to optimize based upon an objective function that generally involves an access to a reservoir simulator. Inexpensive constraints that are not based on computation of the objective function are evaluated prior to accessing the reservoir simulator to avoid unnecessary accesses to the reservoir simulator for candidate well placement plans determined to be infeasible in view of the inexpensive constraints. For candidate well placement plans that are determined to be feasible based upon the inexpensive constraints, the objective function may be calculated and additional expensive constraints may thereafter be evaluated to further determine the feasibility of candidate well placement plans.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/756,800 filed Jan. 25, 2013, which isincorporated herein by reference in its entirety.

BACKGROUND

Well placement planning is used in a number of industries to plan outthe placement of prospective wells. In the oil & gas industry, forexample, well placement planning is used to select placements andtrajectories for proposed wells into a subsurface reservoir to reachspecific locations in the reservoir that are believed to containrecoverable hydrocarbons. Well placement planning may be used to producea well placement plan (WPP) that includes one or more wells, as well asadditional information such as well trajectories, well completions,drilling schedules, etc. Generally, a reservoir simulator is used inconnection with well placement planning so that reservoir simulation maybe performed to determine the potential value of any well placementplan.

Well placement planning may generally be considered to be anoptimization problem. Generally, well placement planning has beenperformed in a predominantly manual process in which a user selectstarget and well locations, performs a reservoir simulation forecast, andthen calculates a value based on the forecast oil or gas recovered andthe cost of the wells. The user generally may repeat the process anumber of times, but modify the number and location of the wells andcompletions. The modifications may include, for example, different waterflooding strategies, well spacing, well types, platform locations, etc.

Well placement planning, however, has been found to be a verytime-consuming process from both the user's perspective and acomputational perspective. Well placement planning has also been foundto be a relatively inefficient process because it may be difficult for auser to objectively explore the complete solution space.

A need therefore exists in the art for a more effective andcomputationally efficient approach to well placement planning

SUMMARY

The embodiments disclosed herein provide a method, apparatus, andprogram product that utilize constrained optimization framework togenerate a well placement plan based on a reservoir model. Candidatewell placement plans are generated from control vectors proposed by anoptimization engine to optimize based upon an objective function thatgenerally involves an access to a reservoir simulator. Constraints thatare not based on computation of the objective function, referred toherein as inexpensive constraints, are evaluated prior to computation ofthe objective function (e.g., by accessing the reservoir simulator) toavoid unnecessary computationally expensive operations for candidatewell placement plans determined to be infeasible in view of theinexpensive constraints. For candidate well placement plans that aredetermined to be feasible based upon the inexpensive constraints, theobjective function may be calculated and additional constraints,referred to herein as expensive constraints, may thereafter be evaluatedto further determine the feasibility of candidate well placement plans.

Therefore, in accordance with some embodiments, a method for wellplacement planning is performed that includes generating a controlvector comprising a plurality of control variables over which tooptimize, translating the control vector to a candidate well placementplan, performing a first feasibility evaluation for the candidate wellplacement plan against one or more inexpensive constraints, and inresponse to determining a feasibility of the candidate well placementplan from the first feasibility evaluation, computing a result for anobjective function based upon the candidate well placement plan using areservoir simulator and performing a second feasibility evaluation forthe candidate well placement plan by evaluating the computed result forthe objective function based upon the candidate well placement planagainst one or more expensive constraints.

In accordance with some embodiments, an apparatus is provided thatincludes at least one processing unit and program code configured uponexecution by the at least one processing unit to perform well placementplanning by generating a control vector comprising a plurality ofcontrol variables over which to optimize, translating the control vectorto a candidate well placement plan, performing a first feasibilityevaluation for the candidate well placement plan against one or moreinexpensive constraints, and in response to determining a feasibility ofthe candidate well placement plan from the first feasibility evaluation,computing a result for an objective function based upon the candidatewell placement plan using a reservoir simulator and performing a secondfeasibility evaluation for the candidate well placement plan byevaluating the computed result for the objective function based upon thecandidate well placement plan against one or more expensive constraints.

In accordance with some embodiments, a program product is provided thatincludes a computer readable medium and program code stored on thecomputer readable medium and configured upon execution by at least oneprocessing unit to perform well placement planning by generating acontrol vector comprising a plurality of control variables over which tooptimize, translating the control vector to a candidate well placementplan, performing a first feasibility evaluation for the candidate wellplacement plan against one or more inexpensive constraints, and inresponse to determining a feasibility of the candidate well placementplan from the first feasibility evaluation, computing a result for anobjective function based upon the candidate well placement plan using areservoir simulator and performing a second feasibility evaluation forthe candidate well placement plan by evaluating the computed result forthe objective function based upon the candidate well placement planagainst one or more expensive constraints.

In accordance with some embodiments, an apparatus is provided thatincludes at least one processing unit, program code and means forperforming well placement planning by generating a control vectorcomprising a plurality of control variables over which to optimize,translating the control vector to a candidate well placement plan,performing a first feasibility evaluation for the candidate wellplacement plan against one or more inexpensive constraints, and inresponse to determining a feasibility of the candidate well placementplan from the first feasibility evaluation, computing a result for anobjective function based upon the candidate well placement plan using areservoir simulator and performing a second feasibility evaluation forthe candidate well placement plan by evaluating the computed result forthe objective function based upon the candidate well placement planagainst one or more expensive constraints.

In accordance with some embodiments, an information processing apparatusfor use in a computing system is provided, and includes means forperforming well placement planning by generating a control vectorcomprising a plurality of control variables over which to optimize,translating the control vector to a candidate well placement plan,performing a first feasibility evaluation for the candidate wellplacement plan against one or more inexpensive constraints, and inresponse to determining a feasibility of the candidate well placementplan from the first feasibility evaluation, computing a result for anobjective function based upon the candidate well placement plan using areservoir simulator and performing a second feasibility evaluation forthe candidate well placement plan by evaluating the computed result forthe objective function based upon the candidate well placement planagainst one or more expensive constraints.

In some embodiments, an aspect of the invention involves performing afeasibility evaluation for the control vector against one or more linearconstraints prior to translating the control vector, where translatingthe control vector is only performed in response to determining afeasibility of the control vector from the third feasibility evaluation.

In some embodiments, an aspect of the invention includes that thecontrol vector comprises an initial control vector, and involvesgenerating the initial control vector by translating an initial wellplacement plan to the initial control vector.

In some embodiments, an aspect of the invention involves, in response todetermining an infeasibility of the candidate well placement plan fromthe first feasibility evaluation, bypassing computing the result for theobjective function and performing the second feasibility evaluation.

In some embodiments, an aspect of the invention involves, in response todetermining a feasibility of the candidate well placement plan from thesecond feasibility evaluation, determining that the candidate wellplacement plan is a feasible well placement plan.

In some embodiments, an aspect of the invention involves, for each of aplurality of control vectors, performing a trial processing operationassociated therewith, where each trial processing operation comprisesdetermining feasibility for the associated control vector against one ormore linear constraints and, in response to determining a feasibility ofthe associated control vector against the one or more linearconstraints, translating the associated control vector to an associatedcandidate well placement plan, performing the first feasibilityevaluation for the associated candidate well placement plan against theone or more inexpensive constraints, and in response to determining afeasibility of the associated candidate well placement plan from thefirst feasibility evaluation, computing a result for the objectivefunction based upon the associated candidate well placement plan usingthe reservoir simulator, and performing the second feasibilityevaluation for the associated candidate well placement plan byevaluating the computed result for the objective function based upon theassociated candidate well placement plan against the one or moreexpensive constraints.

In some embodiments, an aspect of the invention involves generating atleast one of the plurality of control vectors by extrapolating from aprior control vector based at least in part on a feasibility evaluationperformed during a trial processing operation for the prior controlvector.

In some embodiments, an aspect of the invention includes that the priorcontrol vector is associated with an associated candidate well placementplan determined as infeasible, and extrapolating from the prior controlvector is based upon a result of at least one feasibility evaluationperformed during the trial processing operation for the prior controlvector.

In some embodiments, an aspect of the invention involves terminatingwell placement planning after performing the trial processing operationfor each of the plurality of control vectors in response to atermination condition, where the termination condition is based on adetermination that a maximum number of trial processing operations havebeen performed, a determination that improvement in the objectivefunction has stalled, or a combination thereof.

In some embodiments, an aspect of the invention includes that thereservoir simulator comprises an analytical reservoir simulator thataccesses a coarse scale reservoir simulation model.

In some embodiments, an aspect of the invention involves generating thecoarse scale reservoir simulation model by upscaling a fine scalereservoir geology model.

In some embodiments, an aspect of the invention includes that theobjective function includes one or more of net present value, return oninvestment, profitability, production index, or combinations thereof.

In some embodiments, an aspect of the invention includes that computingthe result of the objective function comprises computing a plurality ofresults for a plurality of realizations to account for uncertainty inthe reservoir model, the method further comprising optimizing on autility function based on the plurality of results computed for theplurality of realizations.

In some embodiments, an aspect of the invention includes thattranslating the control vector to the candidate well placement plancomprises identifying a plurality of target locations in a reservoir,determining a completion geometry for each target location, anddetermining a trajectory for each target location.

In some embodiments, an aspect of the invention includes thatdetermining the completion geometry for a first target location amongthe plurality of target locations comprises determining at least onecompletion location based upon at least one property of a plurality ofcells associated with the first target location and retrieved from afine scale reservoir geology model.

In some embodiments, an aspect of the invention includes that the one ormore inexpensive constraints includes a feasibility of the first targetlocation based on a geometric relation to the fine scale reservoirgeology model, where the geometric relation includes a minimumcompletion length, a minimum standoff relative to a fluid contact, aminimum distance to a fault, or a combination thereof.

In some embodiments, an aspect of the invention includes that the one ormore inexpensive constraints includes a feasibility of the first targetlocation based on a property of the fine scale reservoir geology model,where the property includes minimum porosity, minimum permeability,maximum water saturation, or a combination thereof.

In some embodiments, an aspect of the invention includes that performingthe first feasibility evaluation for the candidate well placement planagainst the one or more inexpensive constraints comprises performinganti-collision analysis on the candidate well placement plan.

In some embodiments, an aspect of the invention includes that the one ormore inexpensive constraints includes one or more of dogleg severity,maximum inclination, maximum reach, number of platforms, number ofwells, flowing producers, slot number, platform location, minimum tiepoint separation, minimum completion spacing, or combinations thereof.

In some embodiments, an aspect of the invention includes that the one ormore expensive constraints includes one or more of sub-economic wells,flowing producers or a combination thereof.

In some embodiments, an aspect of the invention includes that thecontrol vector comprises one or more of target location coordinates, tiepoint coordinates, azimuth of a pattern, pattern spacing, orcombinations thereof.

These and other advantages and features, which characterize theinvention, are set forth in the claims annexed hereto and forming afurther part hereof. However, for a better understanding of theinvention, and of the advantages and objectives attained through itsuse, reference should be made to the Drawings, and to the accompanyingdescriptive matter, in which there is described example embodiments ofthe invention. This summary is merely provided to introduce a selectionof concepts that are further described below in the detaileddescription, and is not intended to identify key or essential featuresof the claimed subject matter, nor is it intended to be used as an aidin limiting the scope of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example hardware and softwareenvironment for a data processing system in accordance withimplementation of various technologies and techniques described herein.

FIGS. 2A-2D illustrate simplified, schematic views of an oilfield havingsubterranean formations containing reservoirs therein in accordance withimplementations of various technologies and techniques described herein.

FIG. 3 illustrates a schematic view, partially in cross section of anoilfield having a plurality of data acquisition tools positioned atvarious locations along the oilfield for collecting data from thesubterranean formations in accordance with implementations of varioustechnologies and techniques described herein.

FIG. 4 illustrates a production system for performing one or moreoilfield operations in accordance with implementations of varioustechnologies and techniques described herein.

FIG. 5 is a flowchart illustrating an example sequence of operations fora well placement planning workflow in accordance with implementations ofvarious technologies and techniques described herein.

FIG. 6 is a cross section of an automatically generated vertical wellthrough a reservoir, with three completions corresponding to threefeasible (porous) intervals.

FIG. 7 is a three dimensional model view of a single platform with Swell trajectories connected to targets.

FIG. 8 is a plot of an objective function for a plurality of trials,illustrating the progress of an optimization workflow.

FIG. 9 is an illustration of a feasible region and bounding box used ina target driven vertical wells case study.

FIG. 10 is a three dimensional model view of eight optimized verticalwells in feasible regions above oil water contact in the target drivenvertical wells case study referenced in FIG. 9.

FIG. 11 is a pattern control vector for a five spot pattern in a patterndriven vertical wells case study.

FIG. 12 is a three dimensional model view of an optimized five spotpattern in the pattern driven vertical wells case study referenced inFIG. 11.

DETAILED DESCRIPTION

The herein-described embodiments provide a method, apparatus, andprogram product that implement a constrained optimization framework togenerate a well placement plan based on a reservoir model. Candidatewell placement plans are generated from control vectors proposed by anoptimization engine to optimize based upon an objective function thatgenerally involves an access to a reservoir simulator. Constraints thatare not based on computation of the objective function, referred toherein as inexpensive constraints, are evaluated prior to accessing thereservoir simulator to avoid unnecessary accesses to the reservoirsimulator for candidate well placement plans determined to be infeasiblein view of the inexpensive constraints. For candidate well placementplans that are determined to be feasible based upon the inexpensiveconstraints, the objective function may be calculated and additionalconstraints, referred to herein as expensive constraints, may thereafterbe evaluated to further determine the feasibility of candidate wellplacement plans.

In this regard, a well placement plan, also referred to as a fielddevelopment plan, may be considered to include one or more wellsproposed for a geographic region such as an oilfield, as well asadditional planning information associated with drilling and completingthe wells, including, for example, location and/or trajectoryinformation, completion information, drilling schedule information,projected production information, or any other information suitable foruse in drilling the proposed wells.

A constrained optimization framework, in turn, may be considered toinclude a framework through which a constrained optimization approachmay be applied to the generation of a well placement plan (WPP) in thepresence of uncertainty and risk, based upon one or more reservoirmodels, and based upon a set of constraints that drive the feasibilityof candidate well placement plans developed by the framework.Constraints may be geometric, operational, contractual and/or legal innature, and as discussed in greater detail below, may vary in terms oftheir computational expense. Inexpensive constraints, for example, maygenerally be considered to include constraints that may be evaluatedwithout accessing a reservoir simulator, while expensive constraints maygenerally be considered to include constraints that do involve an accessto a reservoir simulator prior to evaluation. Generally, one or morereservoir simulators are used in the illustrated embodiments in thecomputation of an objective function that drives the optimization to adesired end result, e.g., to maximize net present value, return oninvestment, profitability, production, etc., and well placement plansare associated with control vectors that are used to calculate theobjective function for different well placement plans.

Other variations and modifications will be apparent to one of ordinaryskill in the art.

Hardware and Software Environment

Turning now to the drawings, wherein like numbers denote like partsthroughout the several views, FIG. 1 illustrates an example dataprocessing system 10 in which the various technologies and techniquesdescribed herein may be implemented. System 10 is illustrated asincluding one or more computers 12, e.g., client computers, eachincluding a central processing unit (CPU) 14 including at least onehardware-based processor or processing core 16. CPU 14 is coupled to amemory 18, which may represent the random access memory (RAM) devicescomprising the main storage of a computer 12, as well as anysupplemental levels of memory, e.g., cache memories, non-volatile orbackup memories (e.g., programmable or flash memories), read-onlymemories, etc. In addition, memory 18 may be considered to includememory storage physically located elsewhere in a computer 12, e.g., anycache memory in a microprocessor or processing core, as well as anystorage capacity used as a virtual memory, e.g., as stored on a massstorage device 20 or on another computer coupled to a computer 12.

Each computer 12 also generally receives a number of inputs and outputsfor communicating information externally. For interface with a user oroperator, a computer 12 generally includes a user interface 22incorporating one or more user input/output devices, e.g., a keyboard, apointing device, a display, a printer, etc. Otherwise, user input may bereceived, e.g., over a network interface 24 coupled to a network 26,from one or more external computers, e.g., one or more servers 28 orother computers 12. A computer 12 also may be in communication with oneor more mass storage devices 20, which may be, for example, internalhard disk storage devices, external hard disk storage devices, storagearea network devices, etc.

A computer 12 generally operates under the control of an operatingsystem 30 and executes or otherwise relies upon various computersoftware applications, components, programs, objects, modules, datastructures, etc. For example, a petro-technical module or component 32executing within an exploration and production (E&P) platform 34 may beused to access, process, generate, modify or otherwise utilizepetro-technical data, e.g., as stored locally in a database 36 and/oraccessible remotely from a collaboration platform 38. Collaborationplatform 38 may be implemented using multiple servers 28 in someimplementations, and it will be appreciated that each server 28 mayincorporate a CPU, memory, and other hardware components similar to acomputer 12.

In one non-limiting embodiment, for example, E&P platform 34 mayimplemented as the PETREL Exploration & Production (E&P) softwareplatform, while collaboration platform 38 may be implemented as theSTUDIO E&P KNOWLEDGE ENVIRONMENT platform, both of which are availablefrom Schlumberger Ltd. and its affiliates. It will be appreciated,however, that the techniques discussed herein may be utilized inconnection with other platforms and environments, so the invention isnot limited to the particular software platforms and environmentsdiscussed herein.

In general, the routines executed to implement the embodiments disclosedherein, whether implemented as part of an operating system or a specificapplication, component, program, object, module or sequence ofinstructions, or even a subset thereof, will be referred to herein as“computer program code,” or simply “program code.” Program codegenerally comprises one or more instructions that are resident atvarious times in various memory and storage devices in a computer, andthat, when read and executed by one or more hardware-based processingunits in a computer (e.g., microprocessors, processing cores or otherhardware-based circuit logic), cause that computer to perform the stepsembodying desired functionality. Moreover, while embodiments have andhereinafter will be described in the context of fully functioningcomputers and computer systems, those skilled in the art will appreciatethat the various embodiments are capable of being distributed as aprogram product in a variety of forms, and that the invention appliesequally regardless of the particular type of computer readable mediaused to actually carry out the distribution.

Such computer readable media may include computer readable storage mediaand communication media. Computer readable storage media isnon-transitory in nature, and may include volatile and non-volatile, andremovable and non-removable media implemented in any method ortechnology for storage of information, such as computer-readableinstructions, data structures, program modules or other data. Computerreadable storage media may further include RAM, ROM, erasableprogrammable read-only memory (EPROM), electrically erasableprogrammable read-only memory (EEPROM), flash memory or other solidstate memory technology, CD-ROM, DVD, or other optical storage, magneticcassettes, magnetic tape, magnetic disk storage or other magneticstorage devices, or any other medium that can be used to store thedesired information and which can be accessed by computer 10.Communication media may embody computer readable instructions, datastructures or other program modules. By way of example, and notlimitation, communication media may include wired media such as a wirednetwork or direct-wired connection, and wireless media such as acoustic,RF, infrared and other wireless media. Combinations of any of the abovemay also be included within the scope of computer readable media.

Various program code described hereinafter may be identified based uponthe application within which it is implemented in a specific embodimentof the invention. However, it should be appreciated that any particularprogram nomenclature that follows is used merely for convenience, andthus the invention should not be limited to use solely in any specificapplication identified and/or implied by such nomenclature. Furthermore,given the endless number of manners in which computer programs may beorganized into routines, procedures, methods, modules, objects, and thelike, as well as the various manners in which program functionality maybe allocated among various software layers that are resident within atypical computer (e.g., operating systems, libraries, API's,applications, applets, etc.), it should be appreciated that theinvention is not limited to the specific organization and allocation ofprogram functionality described herein.

Furthermore, it will be appreciated by those of ordinary skill in theart having the benefit of the instant disclosure that the variousoperations described herein that may be performed by any program code,or performed in any routines, workflows, or the like, may be combined,split, reordered, omitted, and/or supplemented with other techniquesknown in the art, and therefore, the invention is not limited to theparticular sequences of operations described herein.

Those skilled in the art will recognize that the example environmentillustrated in FIG. 1 is not intended to limit the invention. Indeed,those skilled in the art will recognize that other alternative hardwareand/or software environments may be used without departing from thescope of the invention.

Oilfield Operations

FIGS. 2A-2D illustrate simplified, schematic views of an oilfield 100having subterranean formation 102 containing reservoir 104 therein inaccordance with implementations of various technologies and techniquesdescribed herein. FIG. 2A illustrates a survey operation being performedby a survey tool, such as seismic truck 106.1, to measure properties ofthe subterranean formation. The survey operation is a seismic surveyoperation for producing sound vibrations. In FIG. 2A, one such soundvibration, sound vibration 112 generated by source 110, reflects offhorizons 114 in earth formation 116. A set of sound vibrations isreceived by sensors, such as geophone-receivers 118, situated on theearth's surface. The data received 120 is provided as input data to acomputer 122.1 of a seismic truck 106.1, and responsive to the inputdata, computer 122.1 generates seismic data output 124. This seismicdata output may be stored, transmitted or further processed as desired,for example, by data reduction.

FIG. 2B illustrates a drilling operation being performed by drillingtools 106.2 suspended by rig 128 and advanced into subterraneanformations 102 to form wellbore 136. Mud pit 130 is used to drawdrilling mud into the drilling tools via flow line 132 for circulatingdrilling mud down through the drilling tools, then up wellbore 136 andback to the surface. The drilling mud may be filtered and returned tothe mud pit. A circulating system may be used for storing, controllingor filtering the flowing drilling muds. The drilling tools are advancedinto subterranean formations 102 to reach reservoir 104. Each well maytarget one or more reservoirs. The drilling tools are adapted formeasuring downhole properties using logging while drilling tools. Thelogging while drilling tools may also be adapted for taking core sample133 as shown.

Computer facilities may be positioned at various locations about theoilfield 100 (e.g., the surface unit 134) and/or at remote locations.Surface unit 134 may be used to communicate with the drilling toolsand/or offsite operations, as well as with other surface or downholesensors. Surface unit 134 is capable of communicating with the drillingtools to send commands to the drilling tools, and to receive datatherefrom. Surface unit 134 may also collect data generated during thedrilling operation and produces data output 135, which may then bestored or transmitted.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various oilfield operations as describedpreviously. As shown, sensor (S) is positioned in one or more locationsin the drilling tools and/or at rig 128 to measure drilling parameters,such as weight on bit, torque on bit, pressures, temperatures, flowrates, compositions, rotary speed, and/or other parameters of the fieldoperation. Sensors (S) may also be positioned in one or more locationsin the circulating system.

Drilling tools 106.2 may include a bottom hole assembly (BHA) (notshown), generally referenced, near the drill bit (e.g., within severaldrill collar lengths from the drill bit). The bottom hole assemblyincludes capabilities for measuring, processing, and storinginformation, as well as communicating with surface unit 134. The bottomhole assembly further includes drill collars for performing variousother measurement functions.

The bottom hole assembly may include a communication subassembly thatcommunicates with surface unit 134. The communication subassembly isadapted to send signals to and receive signals from the surface using acommunications channel such as mud pulse telemetry, electro-magnetictelemetry, or wired drill pipe communications. The communicationsubassembly may include, for example, a transmitter that generates asignal, such as an acoustic or electromagnetic signal, which isrepresentative of the measured drilling parameters. It will beappreciated by one of skill in the art that a variety of telemetrysystems may be employed, such as wired drill pipe, electromagnetic orother known telemetry systems.

Generally, the wellbore is drilled according to a drilling plan that isestablished prior to drilling. The drilling plan sets forth equipment,pressures, trajectories and/or other parameters that define the drillingprocess for the wellsite. The drilling operation may then be performedaccording to the drilling plan. However, as information is gathered, thedrilling operation may need to deviate from the drilling plan.Additionally, as drilling or other operations are performed, thesubsurface conditions may change. The earth model may also needadjustment as new information is collected

The data gathered by sensors (S) may be collected by surface unit 134and/or other data collection sources for analysis or other processing.The data collected by sensors (S) may be used alone or in combinationwith other data. The data may be collected in one or more databasesand/or transmitted on or offsite. The data may be historical data, realtime data or combinations thereof. The real time data may be used inreal time, or stored for later use. The data may also be combined withhistorical data or other inputs for further analysis. The data may bestored in separate databases, or combined into a single database.

Surface unit 134 may include transceiver 137 to allow communicationsbetween surface unit 134 and various portions of the oilfield 100 orother locations. Surface unit 134 may also be provided with orfunctionally connected to one or more controllers (not shown) foractuating mechanisms at oilfield 100. Surface unit 134 may then sendcommand signals to oilfield 100 in response to data received. Surfaceunit 134 may receive commands via transceiver 137 or may itself executecommands to the controller. A processor may be provided to analyze thedata (locally or remotely), make the decisions and/or actuate thecontroller. In this manner, oilfield 100 may be selectively adjustedbased on the data collected. This technique may be used to optimizeportions of the field operation, such as controlling drilling, weight onbit, pump rates or other parameters. These adjustments may be madeautomatically based on computer protocol, and/or manually by anoperator. In some cases, well plans may be adjusted to select optimumoperating conditions, or to avoid problems.

FIG. 2C illustrates a wireline operation being performed by wirelinetool 106.3 suspended by rig 128 and into wellbore 136 of FIG. 2B.Wireline tool 106.3 is adapted for deployment into wellbore 136 forgenerating well logs, performing downhole tests and/or collectingsamples. Wireline tool 106.3 may be used to provide another method andapparatus for performing a seismic survey operation. Wireline tool 106.3may, for example, have an explosive, radioactive, electrical or acousticenergy source 144 that sends and/or receives electrical signals tosurrounding subterranean formations 102 and fluids therein.

Wireline tool 106.3 may be operatively connected to, for example,geophones 118 and a computer 122.1 of a seismic truck 106.1 of FIG. 2A.Wireline tool 106.3 may also provide data to surface unit 134. Surfaceunit 134 may collect data generated during the wireline operation andmay produce data output 135 that may be stored or transmitted. Wirelinetool 106.3 may be positioned at various depths in the wellbore 136 toprovide a survey or other information relating to the subterraneanformation 102.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various field operations as describedpreviously. As shown, sensor S is positioned in wireline tool 106.3 tomeasure downhole parameters which relate to, for example porosity,permeability, fluid composition and/or other parameters of the fieldoperation.

FIG. 2D illustrates a production operation being performed by productiontool 106.4 deployed from a production unit or Christmas tree 129 andinto completed wellbore 136 for drawing fluid from the downholereservoirs into surface facilities 142. The fluid flows from reservoir104 through perforations in the casing (not shown) and into productiontool 106.4 in wellbore 136 and to surface facilities 142 via gatheringnetwork 146.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various field operations as describedpreviously. As shown, the sensor (S) may be positioned in productiontool 106.4 or associated equipment, such as christmas tree 129,gathering network 146, surface facility 142, and/or the productionfacility, to measure fluid parameters, such as fluid composition, flowrates, pressures, temperatures, and/or other parameters of theproduction operation.

Production may also include injection wells for added recovery. One ormore gathering facilities may be operatively connected to one or more ofthe wellsites for selectively collecting downhole fluids from thewellsite(s).

While FIGS. 2B-2D illustrate tools used to measure properties of anoilfield, it will be appreciated that the tools may be used inconnection with non-oilfield operations, such as gas fields, mines,aquifers, storage, or other subterranean facilities. Also, while certaindata acquisition tools are depicted, it will be appreciated that variousmeasurement tools capable of sensing parameters, such as seismic two-waytravel time, density, resistivity, production rate, etc., of thesubterranean formation and/or its geological formations may be used.Various sensors (S) may be located at various positions along thewellbore and/or the monitoring tools to collect and/or monitor thedesired data. Other sources of data may also be provided from offsitelocations.

The field configurations of FIGS. 2A-2D are intended to provide a briefdescription of an example of a field usable with oilfield applicationframeworks. Part, or all, of oilfield 100 may be on land, water, and/orsea. Also, while a single field measured at a single location isdepicted, oilfield applications may be utilized with any combination ofone or more oilfields, one or more processing facilities and one or morewellsites.

FIG. 3 illustrates a schematic view, partially in cross section ofoilfield 200 having data acquisition tools 202.1, 202.2, 202.3 and 202.4positioned at various locations along oilfield 200 for collecting dataof subterranean formation 204 in accordance with implementations ofvarious technologies and techniques described herein. Data acquisitiontools 202.1-202.4 may be the same as data acquisition tools 106.1-106.4of FIGS. 2A-2D, respectively, or others not depicted. As shown, dataacquisition tools 202.1-202.4 generate data plots or measurements208.1-208.4, respectively. These data plots are depicted along oilfield200 to demonstrate the data generated by the various operations.

Data plots 208.1-208.3 are examples of static data plots that may begenerated by data acquisition tools 202.1-202.3, respectively, however,it should be understood that data plots 208.1-208.3 may also be dataplots that are updated in real time. These measurements may be analyzedto better define the properties of the formation(s) and/or determine theaccuracy of the measurements and/or for checking for errors. The plotsof each of the respective measurements may be aligned and scaled forcomparison and verification of the properties.

Static data plot 208.1 is a seismic two-way response over a period oftime. Static plot 208.2 is core sample data measured from a core sampleof the formation 204. The core sample may be used to provide data, suchas a graph of the density, porosity, permeability, or some otherphysical property of the core sample over the length of the core. Testsfor density and viscosity may be performed on the fluids in the core atvarying pressures and temperatures. Static data plot 208.3 is a loggingtrace that generally provides a resistivity or other measurement of theformation at various depths.

A production decline curve or graph 208.4 is a dynamic data plot of thefluid flow rate over time. The production decline curve generallyprovides the production rate as a function of time. As the fluid flowsthrough the wellbore, measurements are taken of fluid properties, suchas flow rates, pressures, composition, etc.

Other data may also be collected, such as historical data, user inputs,economic information, and/or other measurement data and other parametersof interest. As described below, the static and dynamic measurements maybe analyzed and used to generate models of the subterranean formation todetermine characteristics thereof. Similar measurements may also be usedto measure changes in formation aspects over time.

The subterranean structure 204 has a plurality of geological formations206.1-206.4. As shown, this structure has several formations or layers,including a shale layer 206.1, a carbonate layer 206.2, a shale layer206.3 and a sand layer 206.4. A fault 207 extends through the shalelayer 206.1 and the carbonate layer 206.2. The static data acquisitiontools are adapted to take measurements and detect characteristics of theformations.

While a specific subterranean formation with specific geologicalstructures is depicted, it will be appreciated that oilfield 200 maycontain a variety of geological structures and/or formations, sometimeshaving extreme complexity. In some locations, generally below the waterline, fluid may occupy pore spaces of the formations. Each of themeasurement devices may be used to measure properties of the formationsand/or its geological features. While each acquisition tool is shown asbeing in specific locations in oilfield 200, it will be appreciated thatone or more types of measurement may be taken at one or more locationsacross one or more fields or other locations for comparison and/oranalysis.

The data collected from various sources, such as the data acquisitiontools of FIG. 3, may then be processed and/or evaluated. Generally,seismic data displayed in static data plot 208.1 from data acquisitiontool 202.1 is used by a geophysicist to determine characteristics of thesubterranean formations and features. The core data shown in static plot208.2 and/or log data from well log 208.3 are generally used by ageologist to determine various characteristics of the subterraneanformation. The production data from graph 208.4 is generally used by thereservoir engineer to determine fluid flow reservoir characteristics.The data analyzed by the geologist, geophysicist and the reservoirengineer may be analyzed using modeling techniques.

FIG. 4 illustrates an oilfield 300 for performing production operationsin accordance with implementations of various technologies andtechniques described herein. As shown, the oilfield has a plurality ofwellsites 302 operatively connected to central processing facility 354.The oilfield configuration of FIG. 4 is not intended to limit the scopeof the oilfield application system. Part, or all, of the oilfield may beon land and/or sea. Also, while a single oilfield with a singleprocessing facility and a plurality of wellsites is depicted, anycombination of one or more oilfields, one or more processing facilitiesand one or more wellsites may be present.

Each wellsite 302 has equipment that forms wellbore 336 into the earth.The wellbores extend through subterranean formations 306 includingreservoirs 304. These reservoirs 304 contain fluids, such ashydrocarbons. The wellsites draw fluid from the reservoirs and pass themto the processing facilities via surface networks 344. The surfacenetworks 344 have tubing and control mechanisms for controlling the flowof fluids from the wellsite to processing facility 354.

Constrained Optimization for Well Placement Planning

Embodiments consistent with the invention may be used to facilitate wellplacement planning through the use of an optimization framework thatapplies a constrained optimization approach to generate an optimal wellplacement plan based upon an objective function representing a desiredend goal, e.g., net present value, profitability, return on investment,production, etc.

In general, well placement planning is an optimization problem. Itinvolves discovering the optimal wells and completions to attempt tomaximize the value of an asset. As such well placement planning may beframed as a general nonlinear constrained optimization problem, e.g., byminimizing an objective function f(x) subject to:

l _(i) ≦x _(i) ≦u _(i) for i=1, . . . , n  (1)

g _(j)(x)≦0 for j=1, . . . , q  (2)

h _(j)(x)≦0 for j=1, . . . , m  (3)

where

-   -   x={x₁, . . . , x_(n)}⊂        _(n) is a set of n control variables over which to optimize,    -   f:        _(n)→        is the objective function,    -   l, u the lower and upper bounds respectively,    -   g:        ^(n)→        ^(q) the inequality constraints, and    -   h:        ^(n)→        ^(m) the inequality constraints.

The constraint functions (g, h) may be linear or non-linear with respectto the control variables.

A number of approaches exist for discovering the optimal set of controlvariables x, also referred to herein as a control vector that optimizesthe objective function. For example, well placement may be treated as aninteger or a mixed integer problem in which all or some of the controlvariables assume integer values, e.g., if all drilling targets areknown. However, if the target and well tie point locations arecontinuous functions of the surface, overburden and reservoirproperties, then the control variables generally assume continuous realvalues that cannot be treated as an integer or mixed integer problem.

In addition to the control variables being continuous, well placementoptimization problems generally have computationally complex objectiveand constraint functions for which simple functional forms are generallynot available. As such, this problem generally will also not havederivatives of the objective and constraint functions available, becausethe analytical form generally cannot be obtained and the numerical formmay be too noisy to be useful.

In embodiments consistent with the invention, on the other hand, aderivative free optimization approach, e.g., a nonlinear downhillsimplex pattern search algorithm or a stochastic optimization algorithm,may be used. Other optimization techniques that may be used in theembodiments discussed herein include Genetic Algorithms (GA), SimulatedAnnealing (SA), Branch and Bound (B&B), Covariance MatrixAdaptation-Evolution Strategy (CMA-ES), Particle Swarm Optimization(PSO), Spontaneous Perturbation Stochastic Approximation (SPSA),Retrospective Optimization using Hooke Jeeves search (ROHJ), Nelder-Meaddownhill Simplex (N-M), or Generalized Reduced Gradient (GRG) Genetic,among others. The embodiments discussed hereinafter will focus on anonlinear downhill simplex algorithm because of its simplicity androbustness across a wide spectrum of domains; however, it will beappreciated by those of ordinary skill in the art having the benefit ofthe instant disclosure that other optimization algorithms or techniquesmay be used in other embodiments without departing from the spirit andscope of the invention.

With any of the aforementioned optimization algorithms, an optimizationengine generally proposes a control vector, and the objective functionis evaluated. The algorithm then proposes a new “trial” of the controlvector using information from the results of previous trials, with thegoal of selecting a control vector that improves the value of theobjective function. The optimization generally terminates when themaximum number of trials has been evaluated or a desired accuracy of theobjective function and control vector values has been reached.

In optimization problems of this nature, the question of the globalversus local optimum may arise. In global optimization, the true globalsolution to the optimization problem is found. However, globaloptimization is only suitable for problems with a small number ofvariables. When optimizing a problem such as that described herein, itmay be difficult to ascertain whether a global optimum has been found.However, it has been found that there are a number of safeguardsavailable to ensure an answer, if not provably optimal, is not anunreasonable local optimum. The safeguards may include, for example,generating a good initial guess so that the downhill simplex engine hasa good starting point, and when an optimum solution has been found, theoptimal control vector can be used as an initial guess for a repeatoptimization, with such nested optimizations optionally repeated untilno substantial improvement in the optimum is found.

The general downhill simplex method is an unconstrained optimizationtechnique in which the elements of the control vector x are unbounded.However, well placement optimization has been found to be a highlyconstrained problem in which the control vector elements are not onlybounded as shown in equation (1) but also subjected to linear andnon-linear constraints as shown in equations (2) and (3).

To extend the nonlinear downhill simplex method to support constrainedoptimization a sequential lexicographic approach may be used, where theoriginal problem is reformulated into another minimization problem inwhich the original objective function f(x) is minimized subject toΦ(x)≦0, where the constraint violation function Φ(x) is strictlypositive for infeasible control vectors and less than or equal to zerofor feasible ones, that is:

Φ(x)>0 if x∉

Φ(x)≦0 if x∈

where

-   -   is the feasible region.

In this transformed problem, control vectors may be compared using thelexicographic order comparison operator (<_(CL)) rather than simplecomparison of the objective function values, that is:

$ {( {f_{1},\Phi_{1}} ) <_{CL}( {f_{2},\Phi_{2}} )}\Leftrightarrow\{ \begin{matrix}{if} & {( {x_{1} \notin {\bigvee x_{2}} \notin } ):{\Phi_{1} < \Phi_{2}}} \\{else} & {f_{1} < f_{2}}\end{matrix}  $

This approach may be further refined in the hereinafter-describedembodiments to distinguish between inexpensive and expensiveconstraints, particularly where an objective function evaluation iscomputationally expensive. Inexpensive constraints may be considered tobe constraints for which the feasibility can be determined before theobjective function is evaluated or otherwise without using results ofthe objective function in the determinations, while expensiveconstraints may be considered to be constraints determined after theobjective function is evaluated or otherwise using results of theobjective function in the determinations. Reformulating the problem inthis manner allows for a reduction in the number of evaluations of arelatively expensive objective function, and a new lexicographicsequential order comparison operator (<_(SL)) may be defined as follows:

$ {( {f_{1},\Phi_{l\; 1},\Phi_{{nI}\; 1},\Phi_{{nE}\; 1}} ) <_{SL}( {f_{2},\Phi_{l\; 2},\Phi_{{nI}\; 2},\Phi_{{nE}\; 2}} )}\Leftrightarrow\{ \begin{matrix}{if} & {( {x_{1} \notin {_{l}\bigvee x_{2}} \notin _{l}} ):{\Phi_{l\; 1} < \Phi_{l\; 2}}} \\{{else}\mspace{14mu} {if}} & {( {x_{1} \notin {_{nI}\bigvee x_{2}} \notin _{nI}} ):{\Phi_{{nI}\; 1} < \Phi_{{nI}\; 2}}} \\{{else}\mspace{14mu} {if}} & {( {x_{1} \notin {_{nE}\bigvee x_{2}} \notin _{nE}} ):{\Phi_{{nE}\; 1} < \Phi_{{nE}\; 2}}} \\{else} & {f_{1} < f_{2}}\end{matrix}  $

Put another way, when an optimization engine compares two controlvectors x₁ and x₂, feasibility with respect to the linear constraints

_(l) may first be determined. If either vector is infeasible then thevector with the lower constraint violation function (Φ) is determined tobe better, and no further comparisons may be made. This comparison maythen be repeated, but with respect to non-linear inexpensive constraints

_(nI), and thereafter if necessary with respect to non-linear expensiveconstraints

_(nE). If both vectors are determined to be feasible with respect to allof these constraints then the objective function values may be compareddirectly.

Now turning to FIG. 5, an example well placement planning workflow 400in accordance with implementations of various technologies andtechniques described herein is illustrated, to perform well placementplanning the presence of a geological model of a reservoir. Workflow 400may utilize a framework that automatically generates an optimal WellPlacement Plan (WPP) based on a reservoir model, and in the illustratedembodiment a suite of high-speed computational components generallyallows a WPP to be generated quickly (e.g., in minutes).

Workflow 400 may be used to automate the process of placing new wells ina reservoir and/or sidetracking or recompleting existing wells, and doesso using constraint-based optimization techniques. As will become moreapparent below, optimization of a WPP using one embodiment of workflow400 may utilize a constrained downhill simplex approach. During a trial,WPP's proposed by an optimization engine in earlier trials may beextrapolated to propose a new WPP. A proposed WPP may be evaluated forsatisfying a range of geometric, operational, contractual and legalconstraints on the surface, and in the overburden and reservoir.Collision and hazard avoidance computation may also use a geocomputationtopology approach. When a feasible WPP is discovered a productionforecast may be computed using high-speed (e.g., in seconds) reservoirsimulator that analytically computes pressure and explicitly computessaturation. In addition to recovery, a variety of additional objectivefunctions, e.g., Net Present Value, Return on Investment, ProfitabilityIndex, Maintain Production Rate, etc. may also be used. Optimization inthe presence of subsurface uncertainty may also be considered by usingan ensemble of reservoir models.

Specifically, as will be discussed in greater detail below, workflow 400is dominated by a loop that generally involves the creation of a controlvector by an optimization engine, the translation of this control vectorinto a WPP, the feasibility constraints analysis of that WPP, and theevaluation of the objective function for the WPP. A single pass throughthe loop is termed a “trial,” and this sequence of steps is termed atrial processing operation or element. The optimization engine, in thiscase, the constrained downhill simplex discussed previously, thenproposes a new control vector with the intention of discovering anoptimal control vector. The optimization loop is then complete when oneor more termination conditions is satisfied.

Workflow 400 may be implemented, for example, at least in part withinpetro-technical module 32 of FIG. 1, which may be implemented as, orotherwise access an optimization engine. Module 32 may also access oneor more reservoir simulators (e.g., resident in E&P platform 34) for usein accessing one or more reservoir models. It will be appreciated bythose of ordinary skill in the art having the benefit of the instantdisclosure that some operations in workflow 400 may be combined, split,reordered, omitted and/or supplemented with other techniques known inthe art, and therefore, the invention is not limited to the particularworkflow illustrated in FIG. 5.

Referring again to FIG. 5, workflow 400 may incorporate someinitialization operations, including, as illustrated in block 402, areservoir upscaling operation. The reservoir upscaling operation may beperformed, for example, to upscale one or more fine scale or highresolution geology models 404 to generate a coarse scale or lowresolution simulation model suitable for use by an analytical reservoirsimulator when computing an objective function, such that computation ofthe objective function may be performed using a high-speed (e.g., inseconds) reservoir simulation. Additional initialization operations,e.g., parsing existing wells and geologic hazards in the overburden forcollision avoidance, may also be performed.

Thereafter, block 402 passes control to block 408 to generate an initialguess control vector 410, which is then processed by a trial processingelement 412, which upon completion of a trial, passes control to block414 to generate another control vector 410. Control vectors and theirassociated trial results, including feasibility or infeasibility withrespect to various constraints and the magnitudes of suchfeasibility/infeasibility, may also be maintained in a database or otherdata storage as illustrated at 416.

With respect to creation of a control vector in blocks 408 and 414, acontrol vector may be implemented as a vector of control variables, thatis:

x={x ₁ , . . . , x _(n)}⊂

^(n)

where each control variable assumes a value in the range:

0≦x _(i)≦1.

The optimization engine in general may be unaware of the domain andphysical meaning of each control variable. It is, however, one role ofthe trial processing element 412 of the workflow to analyze the controlvector, generate a WPP and inform the optimization engine of thefeasibility and objective function values.

To generate an “initial guess” control vector in block 408, randomnumbers may be assigned in some embodiments, although in some instances,doing so may be inefficient as generally some knowledge of feasible andfavorable values for at least some of the control variables will beknown at the outset. In other embodiments, however, an initial guesscontrol vector may be generated from an initial WPP from candidatetarget and platform tie point locations, in an operation that iseffectively the inverse of generating a WPP from a control vector (whichis performed in block 420, discussed below).

Targets for the initial control vector may be selected with criteriaunder a user's control. For example, it may be favorable to use targetsnear the crest of anticlines, or focus on regions with the maximumproductivity index, or minimum water saturation. Other manners ofgenerating an initial control vector will be appreciated by one ofordinary skill in the art having the benefit of the instant disclosure.

Next, turning to trial processing element 412, a trial is initiated fora control vector by performing a feasibility evaluation for the controlvector against one or more linear constraints in block 418. For someworkflows, control variables may map directly to tie point or targetlocations, so in these cases, the control variables' values may betransformed directly into project coordinates and evaluated forinclusion or exclusion in the project's region of interest. If a controlvector is determined to be infeasible as a result of this evaluation,trial processing ends for the control vector and control passes to block414 to generate a new control vector.

If feasible, however, the control vector advances to the next stage ofcreating a candidate WPP, as illustrated by block 420, which may also bereferred to as translating the control vector into a candidate WPP. Inthis operation, target identification, trajectory creation andcompletion creation are performed for one or more wells based upon thecontrol variables in the control vector to generate a WPP 422.

Target identification generally refers to identification of targetlocations in a reservoir. For some workflows, some of the controlvariables in a control vector may correspond directly to targetedlocations (X, Y). In such embodiments, the high-resolution, or finescale, geological model 404 may be analyzed to extract the cellscorresponding to each targeted location (e.g., as illustrated byeffective porosity and water saturation columns 450, 452 in FIG. 6). Fora vertical well, this generally corresponds to the cells including theX, Y coordinate. It will be appreciated that the extraction of cells,and in particular, the properties associated with such cells, issubstantially less computationally-expensive than running a numericalsimulation with a high-resolution geological model. Consequently, highresolution reservoir data may be accessed in connection with generatinga WPP in a computationally-efficient manner.

In addition, the completion geometry corresponding to each location mayalso be identified. A user may supply constraints that are used in theconstruction of the completion. For example, to be feasible, acompletion generally has a minimum length and a minimum standoff from afluid contact (e.g., as shown by completions 454, 456 and 458 in FIG.6). Cells may also have valid properties such as minimum permeability,or maximum water saturation. Generally, a completion is created if thesecriteria are satisfied.

Once the target locations and completions have been created from thecontrol vector then the trajectories that connect the completions to thesurface may be created. The control vector generally includes eitherexplicit or implicit tie point location information. For example, if anexisting platform is to be used for a trajectory, the tie point will bepart of the problem definition and not included in the control vector. Atrajectory may then be constructed which connects the tie point to thetarget (e.g., as illustrated by trajectory 460 coupled to target 462 inFIG. 7).

Returning to FIG. 5, once WPP 422 is generated in block 420, block 424then performs an evaluation of the WPP against one or more inexpensiveconstraints. As noted above, the inexpensive constraints may beconstraints on the WPP that may be evaluated without computing theobjective function.

For example, one type of inexpensive constraint is related toanti-collision. A brownfield by definition contains existing wells, andas these existing wells may be actively flowing, abandoned, or acombination, when new wells are proposed it may be desirable to performanti-collision or hazard avoidance analysis to evaluated whether anywell trajectories collide with existing wells or other hazards in thereservoir (e.g., natural hazards). An anti-collision analysis may beimplemented, for example, in the manner disclosed in U.S. ProvisionalApplication No. 61/756,789 filed on Jan. 25, 2013 by Peter Tilke, theentire disclosure of which is incorporated by reference herein. Suchanalysis may therefore be performed in connection with feasibilityconstraint evaluations to ensure the wells in a WPP avoid existing wellsand other hazards.

Another type of inexpensive constraint may be related to a trajectory.For example, dogleg severity, maximum inclination and maximum reach maybe used to limit the tie points that may feasibly connect with a target.

Another type of inexpensive constraint may be evaluated for a targetlocation based on one or more geometric relations between the targetlocation and the high resolution reservoir geology model. Thesegeometric relations may include, but are not limited to, geometricrelations such as minimum completion length, minimum standoff relativeto a fluid contact, minimum distance to a fault, or combinationsthereof. Yet another type of inexpensive constraint may be evaluated fora target location based on one or more properties of the high resolutionreservoir geology model. These properties may include, but are notlimited to, minimum porosity, minimum permeability, maximum watersaturation or combinations thereof.

Additional inexpensive constraints may include:

Number of platforms—have the correct number of platforms been created inthis WPP?Number of wells—have the correct number of wells been created in thisWPP?Flowing producers—does the WPP result in flowing producers existing inthe field?Slot number—each new and existing platform has user specified limits onthe desired minimum and maximum number of utilized slots. The wellsassigned to each platform should satisfy this criterion.Platform location—is each tie point in a valid location? This includeswhether or not the platform is located in a valid area, or avoids asurface hazard, e.g., a steep slope or a riverbed.Minimum tie point separation—tie points meet a minimum spacing from oneanother as specified by a user.Minimum completion spacing—completions meet a minimum spacing from oneanother as specified by a user.

Other inexpensive constraints that may be utilized to evaluate thefeasibility of a well placement plan without computation of theobjective function will be appreciated by one of ordinary skill in theart having the benefit of the instant disclosure. In addition, it willbe appreciated that, in response to a well placement plan beingdetermined to be infeasible based upon the inexpensive constraints,block 424 terminates the trial for the current candidate control vectorand returns control to block 414 to generate a new control vector. Assuch, the computational expense of computing the objective function forthis WPP is avoided.

If, however, the WPP is still determined to be feasible after performingfeasibility evaluation against the inexpensive constraints, block 424passes control to block 426 to compute the objective function. It willbe appreciated that optimization conventionally seeks to discover thefeasible control vector yielding the minimum objective function value.In well placement planning, generally the desire is to maximize anobjective function value. As such, in the illustrated embodiment, thecomputed value is negated before returning the value to the optimizationengine.

In general, different workflows have different objectives, and thereforedifferent objective functions may be used in different embodiments. Forexample, one objective may be to simply maximize recovery, in which casecapital and operating costs along with oil or gas price may be ignored.This may also be the case if the objective is to maintain a plateauproduction rate. A more complete financial objective function may beused in some embodiments to calculate net present value (NPV) in which aforecast recovery, a commodity price, and the costs are considered alongwith a discount factor. Other objective functions that may be usedinclude, for example, fiscal parameters such as return on investment(ROI) and profitability index.

Costs may be separated into capital and operating expenses. Capitalexpenses may include drilling, and surface facility, drilling, well, andcompletion construction. Operating expenses may include personnel,injection, production and treatment costs. Generally, the one componentthat adds value to the objective function is the oil or gas recoveredfrom the reservoir, and everything else is cost. While a user mayprovide an estimate of a forecast commodity price, the productionforecast itself generally is computed.

As noted above, the objective function is computed in block 426 wheneverthe proposed WPP in a trial satisfies the inexpensive constraints.Otherwise, computation of the objective function, and evaluation ofexpensive constraints (discussed below) are bypassed. From acomputational perspective the objective function computation, e.g., aproduction forecast calculation, is generally the most computationallyexpensive part of a trial. For this reason, a high-speed analyticalreservoir simulator, utilizing coarse scale model 406, may be used tocompute the forecast. In one embodiment, the analytical reservoirsimulator may be founded on the analytical solution of the diffusionequation:

$\frac{\partial p}{\partial t} = {{\eta_{x}\frac{\partial^{2}p}{\partial x^{2}}} + {\eta_{y}\frac{\partial^{2}p}{\partial y^{2}}} + {\eta_{z}\frac{\partial^{2}p}{\partial z^{2}}}}$

The simulator may be subject to initial and boundary conditions.Iso-parametric transformation may be used to extend the solution toirregular non-cuboid reservoirs. Regional-scale reservoir heterogeneitymay be modeled with multiple cuboids with differing reservoir rockproperties. Individual wells may refine the modeled heterogeneityfurther through the skin factor (S), which may influence theproductivity index (PI) as follows:

${P\; I} = \frac{{kk}_{ro}h}{{\mu_{o}B_{o}{\ln ( {r_{e}/r_{w}} )}} + S}$

Also, in some embodiments, a pressure analytical saturation explicit(PASE) method may be used to extend the solution to waterfloodingproblems.

Other objective functions and manners of computing the same, includingapproaches that utilize coarse scale models and/or analyticalsimulators, as well as other approaches that do not utilize suchtechniques, or that utilize numerical or other types of reservoirsimulators, may be used in other embodiments, and will be apparent toone of ordinary skill in the art having the benefit of the instantdisclosure.

Once the objective function is computed for a candidate WPP, block 426passes control to block 428 to perform a feasibility evaluation of thecandidate WPP against a set of expensive constraints. In particular,after the objective function has been computed is may be possible insome embodiments that some wells in the WPP are flowing at sub-economicrates. The WPP may therefore be evaluated to remove sub-economic wells.The WPP may then be evaluated to ensure that flowing producers stillremain in the solution.

Other expensive constraints that may be evaluated in other embodimentsinclude, for example, determining that a proposed WPP is infeasible ifno feasible producers exist but only feasible injectors exist, as wellas others that will be appreciated by those of ordinary skill in the arthaving the benefit of the instant disclosure.

If the candidate WPP is determined to be infeasible in block 428,control returns to block 414 to generate a new control vector.Otherwise, the WPP is added to a set of feasible WPP's 430, and controlpasses to block 432 to determine whether the optimization is complete.If not, control passes to block 414 to generate another control vector.If so, control passes to block 434 to terminate the workflow and returnresults to the user.

Trial processing element 412 may therefore be repeated by theoptimization engine until an optimal solution is discovered, orotherwise until another termination condition is met. In addition, asillustrated by block 416, optimization engine uses information garneredfrom control vectors, both infeasible and feasible, to extrapolate newcontrol vectors from past trials. In addition, when the terminationcondition is met, feasible control vectors are reported back as resultsto the user, representing the viable well placement plans determinedfrom the well placement planning workflow.

FIG. 8, for example, illustrates a plot of objective function results(here, value) computed for a plurality of trials. In some embodiments,the plot of FIG. 8 may be progressively generated and displayed to auser during the workflow, with updates made for each feasible WPP addedto the results. As such, a user may view the improvement in theobjective function over the course of the workflow. FIG. 8 alsoillustrates at about trial 60 where the optimization reaches a plateauand supplies the optimum as a new initial guess for a new “restarted”optimization that eventually yields a more-improved value, just one typeof potential optimization technique that may be used by an optimizationengine consistent with the invention.

Block 432 may terminate workflow 400 in response to differenttermination conditions. For example, in one embodiment, a terminationcondition may be based on a determination that a maximum specifiednumber of trials has been completed. In another embodiment, atermination condition may be based on achieving an objective functionvalue that ceases to improve with successive trials within a specifiedaccuracy, or put another way, a determination that improvement in theobjective function has stalled (e.g., insufficient improvement hasoccurred over a most recent set of trials as prescribed by a tolerance).In other embodiments, a combination of determinations may be made, e.g.,to terminate after the objective function does not improve more than X %over the last Y trials, but in any event never exceed Z total trials.

Embodiments consistent with the invention may also optimize in thepresence of uncertainty. During uncertain optimization, an optimalcontrol vector is being sought when the underlying model is uncertain.In the case of well placement planning, the model may be represented bythe overburden and the reservoir, and during optimization, theuncertainty in the model may be reflected in an uncertainty in theobjective function value. Under such conditions, the overalloptimization workflow may remain the same, and function in essentiallythe same manner as illustrated in FIG. 5 as with deterministicoptimization. However, for uncertain optimization, the value of theobjective function being minimized may be considered to be a function ofthe uncertainty distribution in the objective function value. Forexample, the objective function value may have statistical moments suchas mean (μ) and variance (σ²). The optimization engine may attempt tomaximize a single value, which is now a function of these statisticalmoments. This function may be referred to as a “utility function.” Oneutility function that may be used for this type of problem is defined asfollows:

ƒ_(λ)=μ−λσ

where μ and σ are respectively the mean and standard deviation of theobjective function value resulting from the uncertain model, λ is therisk aversion factor, and ƒ_(λ) is the risk corrected objective functionvalue. Optimization then involves maximizing ƒ_(λ).

The risk aversion factor (λ) may be a user-defined preference, and maybe roughly considered equivalent to a confidence level. If, for a givencontrol vector the uncertain objective function value were to benormally distributed this would be precisely true. For example, if λ=0there would be a 50% probability that the objective function value f₀would be greater than the mean μ, so an optimum median (50% confidencelevel) would be obtained by maximizing θ₀. If λ=1, there would be an 84%probability that the realized objective function value would be greaterthan ƒ₁. Therefore, it can be seen that a higher value for λ generallyimplies a more conservative decision.

For well placement planning problems, the underlying overburden andreservoir models are generally complex and the uncertainty in thesemodels is also generally complex and nonlinear. The uncertainty in themodel may therefore be represented as a plurality of realizations of themodel in some embodiments. For example, one may be uncertain in theorientation of turbidite channels in a reservoir, and as such, multiple(N) realizations of the reservoir model may be generated, each with alikely channel orientation and geometry. The goal would be to have thecollection of models reflect the possible spectrum of channelorientations. During optimization, a given control vector yielding a WPPmay result in a different objective function value for each modelrealization. The mean and standard deviation in the objective functionvalue for this collection of models may be generated during optimizationand used to compute f_(λ), the risk corrected objective function value.During uncertain optimization, the objective function is generallyevaluated N times during every trial, which may result in a significantcomputational overhead during uncertain optimizations, and furtherproviding additional benefits when such computations are avoided as aresult of feasibility evaluations that declare a WPP infeasible prior tocomputation of an objective function.

Case Study—Target Driven Vertical Wells

As one example of the herein-described embodiments, consider the problemof finding an optimal placement of vertical wells driven by targetquality. The control variables that make up the control vector may bedirectly associated with target coordinates. For this exercise, theeasting and northing (X, Y) of the target locations may be considered. Avertical well at this location may potentially penetrate the entirereservoir being considered. Thus, to define a target location and hencea vertical well, a control vector may be defined including two controlvariables, one for X and one for Y. For this example consider eighttargets, or vertical wells. If M represents the number of targets, thenthe length of the control vector (N) is given by N=2M. It then followsthat:

x _(j) =X _(2(j-1)+1) and y _(j) =X _(2(j-1)+2) for j=1, . . . , M

where X is the control vector and x_(j), and y_(j) are the coordinatesof the jth target.

As noted above, each control variable may have the following bounds:

0≦X _(i)≦1 for i=1, . . . , N

These values may be mapped to the bounds of a feasible region of thecontrol variable, as illustrated in FIG. 9. Each candidate target mayhave a feasible region (e.g., region 470) defined by an irregularpolygon (or polygons). A rotated bounding box 472 encloses the feasibleregion, and the axes of the bounding box correspond to the two controlvariables defining the target coordinate (x_(j), and y_(j)). A mappingfrom the control variable coordinate system to the project geographiccoordinate system is then a straightforward rotation, scaling andtranslation.

FIG. 10 illustrates the result of optimizing 8 vertical wells 480 in ananticlinal structure. Since M=8 in this example, the total number ofcontrol variables is 16. While production for these 8 producers iscomputed by the reservoir simulator operating on the upscaled reservoirmodel, the productivity of each well is influenced by the fine scaledheterogeneity of the geological model as illustrated here in FIG. 10 bythe permeability property represented by cells 482. Also, note thedistribution of the wells that reflects the distribution in reservoirquality rock, avoidance of infeasible regions (water table), andminimizes the interference between the wells.

Case Study—Target Driven Deviated Wells

The next example is also dictated by target quality. However, ratherthan having vertical wells, this example illustrates the optimizationwith a single platform and four deviated S-Wells (e.g., as shown in FIG.7). In this case, the number of targets (M) is 4 yielding 8 controlvariables to describe the targets, as in the vertical well example.However, the tie point location for the platform may also be specified,thereby requiring an additional two control variables for total of 10.

Case Study—Pattern Driven Vertical Wells

In another example, a pattern driven strategy, specifically a five spotpattern, is illustrated in FIG. 11. In this case discovering the optimalpattern parameters is generally more of an issue that identifyingspecific targets. For basic pattern geometry, the following parametersmay be discovered, as illustrated in FIG. 11:

-   490—Tie point location of one well (2 control variables)-   492—Azimuth of the pattern (1 control variable)-   494—Pattern spacing (1 control variable)

Thus, a basic five spot pattern may be optimized with as few as fourcontrol variables. This can also be made more complex if one allows foran asymmetric aspect ratio in the pattern, or deviated wells as in theprevious example. An illustration of an optimized five spot pattern isshown in FIG. 12.

Presented herein therefore is a framework for automated well placementplanning as part of the field development planning workflow that in someembodiments may be performed quickly and using modest computingresources (e.g., performed in minutes using desktop hardware andsoftware). The framework in some embodiments automatically designs awell placement plan that optimizes an objective function (e.g., NPV orrecovery) in the presence of subsurface uncertainty and operational risktolerance. Also, in some embodiments, a production forecast of the wellplacement plan may also be computed rigorously with an analytical orsemi-analytical reservoir simulator. Engineering, financial, operationaland geological constraints may also be incorporated into the computedplan.

The aforementioned methodology has many applications in the field ofdevelopment planning context. For example, in some embodiments, multiplefield development planning scenarios can be rapidly screened, and may beused in connection with selecting new wells, sidetracking existing wellsand/or completing existing wells. In brownfields with hundreds ofexisting wells, infill locations can be quickly identified. Additionalapplications and uses of the herein-described techniques will beapparent to one of ordinary skill in the art having the benefit of theinstant disclosure.

While particular embodiments have been described, it is not intendedthat the invention be limited thereto, as it is intended that theinvention be as broad in scope as the art will allow and that thespecification be read likewise. It will therefore be appreciated bythose skilled in the art that yet other modifications could be madewithout deviating from its spirit and scope as claimed.

What is claimed is:
 1. A method for well placement planning, the methodcomprising: generating a control vector comprising a plurality ofcontrol variables over which to optimize; translating the control vectorto a candidate well placement plan; performing a first feasibilityevaluation for the candidate well placement plan against one or moreinexpensive constraints; and in response to determining a feasibility ofthe candidate well placement plan from the first feasibility evaluation:computing a result for an objective function based upon the candidatewell placement plan using a reservoir simulator; and performing a secondfeasibility evaluation for the candidate well placement plan byevaluating the computed result for the objective function based upon thecandidate well placement plan against one or more expensive constraints.2. The method of claim 1, further comprising performing a feasibilityevaluation for the control vector against one or more linear constraintsprior to translating the control vector, wherein translating the controlvector is only performed in response to determining a feasibility of thecontrol vector from the third feasibility evaluation.
 3. The method ofclaim 1, wherein the control vector comprises an initial control vector,and wherein the method further comprises generating the initial controlvector by translating an initial well placement plan to the initialcontrol vector.
 4. The method of claim 1, further comprising, inresponse to determining an infeasibility of the candidate well placementplan from the first feasibility evaluation, bypassing computing theresult for the objective function and performing the second feasibilityevaluation.
 5. The method of claim 1, further comprising, in response todetermining a feasibility of the candidate well placement plan from thesecond feasibility evaluation, determining that the candidate wellplacement plan is a feasible well placement plan.
 6. The method of claim1, further comprising, for each of a plurality of control vectors,performing a trial processing operation associated therewith, whereineach trial processing operation comprises: determining feasibility forthe associated control vector against one or more linear constraints;and in response to determining a feasibility of the associated controlvector against the one or more linear constraints: translating theassociated control vector to an associated candidate well placementplan; performing the first feasibility evaluation for the associatedcandidate well placement plan against the one or more inexpensiveconstraints; and in response to determining a feasibility of theassociated candidate well placement plan from the first feasibilityevaluation: computing a result for the objective function based upon theassociated candidate well placement plan using the reservoir simulator;and performing the second feasibility evaluation for the associatedcandidate well placement plan by evaluating the computed result for theobjective function based upon the associated candidate well placementplan against the one or more expensive constraints.
 7. The method ofclaim 6, further comprising, generating at least one of the plurality ofcontrol vectors by extrapolating from a prior control vector based atleast in part on a feasibility evaluation performed during a trialprocessing operation for the prior control vector.
 8. The method ofclaim 7, wherein the prior control vector is associated with anassociated candidate well placement plan determined as infeasible, andwherein extrapolating from the prior control vector is based upon aresult of at least one feasibility evaluation performed during the trialprocessing operation for the prior control vector.
 9. The method ofclaim 7, further comprising terminating well placement planning afterperforming the trial processing operation for each of the plurality ofcontrol vectors in response to a termination condition, wherein thetermination condition is based on a determination that a maximum numberof trial processing operations have been performed, a determination thatimprovement in the objective function has stalled, or a combinationthereof.
 10. The method of claim 1, wherein the reservoir simulatorcomprises an analytical reservoir simulator that accesses a coarse scalereservoir simulation model.
 11. The method of claim 10, furthercomprising generating the coarse scale reservoir simulation model byupscaling a fine scale reservoir geology model.
 12. The method of claim1, wherein the objective function includes one or more of net presentvalue, return on investment, profitability, production index, orcombinations thereof.
 13. The method of claim 1, wherein computing theresult of the objective function comprises computing a plurality ofresults for a plurality of realizations to account for uncertainty inthe reservoir model, the method further comprising optimizing on autility function based on the plurality of results computed for theplurality of realizations.
 14. The method of claim 1, whereintranslating the control vector to the candidate well placement plancomprises identifying a plurality of target locations in a reservoir,determining a completion geometry for each target location, anddetermining a trajectory for each target location.
 15. The method ofclaim 14, wherein determining the completion geometry for a first targetlocation among the plurality of target locations comprises determiningat least one completion location based upon at least one property of aplurality of cells associated with the first target location andretrieved from a fine scale reservoir geology model.
 16. The method ofclaim 15, wherein the one or more inexpensive constraints includes afeasibility of the first target location based on a geometric relationto the fine scale reservoir geology model, wherein the geometricrelation includes a minimum completion length, a minimum standoffrelative to a fluid contact, a minimum distance to a fault, or acombination thereof.
 17. The method of claim 15, wherein the one or moreinexpensive constraints includes a feasibility of the first targetlocation based on a property of the fine scale reservoir geology model,wherein the property includes minimum porosity, minimum permeability,maximum water saturation, or a combination thereof.
 18. The method ofclaim 1, wherein performing the first feasibility evaluation for thecandidate well placement plan against the one or more inexpensiveconstraints comprises performing anti-collision analysis on thecandidate well placement plan.
 19. The method of claim 1, wherein theone or more inexpensive constraints includes one or more of doglegseverity, maximum inclination, maximum reach, number of platforms,number of wells, flowing producers, slot number, platform location,minimum tie point separation, minimum completion spacing, orcombinations thereof.
 20. The method of claim 1, wherein the one or moreexpensive constraints includes one or more of sub-economic wells,flowing producers or a combination thereof.
 21. The method of claim 1,wherein the control vector comprises one or more of target locationcoordinates, tie point coordinates, azimuth of a pattern, patternspacing, or combinations thereof.
 22. An apparatus, comprising: at leastone processing unit; and program code configured upon execution by theat least one processing unit to perform well placement planning by:generating a control vector comprising a plurality of control variablesover which to optimize; translating the control vector to a candidatewell placement plan; performing a first feasibility evaluation for thecandidate well placement plan against one or more inexpensiveconstraints; and in response to determining a feasibility of thecandidate well placement plan from the first feasibility evaluation:computing a result for an objective function based upon the candidatewell placement plan using a reservoir simulator; and performing a secondfeasibility evaluation for the candidate well placement plan byevaluating the computed result for the objective function based upon thecandidate well placement plan against one or more expensive constraints.23. A program product, comprising: a computer readable medium; andprogram code stored on the computer readable medium and configured uponexecution by at least one processing unit to perform well placementplanning by: generating a control vector comprising a plurality ofcontrol variables over which to optimize; translating the control vectorto a candidate well placement plan; performing a first feasibilityevaluation for the candidate well placement plan against one or moreinexpensive constraints; and in response to determining a feasibility ofthe candidate well placement plan from the first feasibility evaluation:computing a result for an objective function based upon the candidatewell placement plan using a reservoir simulator; and performing a secondfeasibility evaluation for the candidate well placement plan byevaluating the computed result for the objective function based upon thecandidate well placement plan against one or more expensive constraints.